Re: 5-Tone Mode of BP Scale/correction

just like how partch added on to his 31 tone diamond to get his 43 tone scale, you have to add the pitches in question.
The point is though it shows how one can make a diamond out of a scale on something besides the octave, which i am sorry that you missed. it offer the same process with other triad, tetrads etc. with various point of equivalence.

one of the simplest , although quite musical method is to take the MOS you scales implies as being next, count out that many tones and take the number of tones in your scale as a subset.
for instance with 12 ET we could consider the next MOS being 19 if we were yassar.
one then take 19 tones, which forms the octave and fifth and take a 12 tone subset of this.
now if we take this idea further
One could take the 13 tone BP scale and find the next constant structure and create another point of equivalence within this already different one.
>Message: 4 > Date: Tue, 06 Dec 2005 19:34:31 -0000
> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
>Subject: Re: 5-Tone Mode of BP Scale
>
>--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> >
>>i thought i would remind others that the BP scale can be considered a >>diamond with a unique interval of equivalence
>>http://www.anaphoria.com/images/BPdiamond.gif
>> >>
>
>I don't understand this, since there are only 7 distinct pitch classes >in a 3-by-3 diamond. The vertical spine consists of three identical >pitches, which you seem to label as '3' or equivalently as '1' (the >other factors cancel out). But the BP diatonic scale has *9* pitch >classes. You could get to it by adding 25/21 and 25/9 to your diamond.
>
> >
>>also of interest is
>>http://www.anaphoria.com/images/BPdia2.gif
>> >>
>
>These seems to merely add more 'tritave equivalents' of the 7 pitch >classes above, but it's still 7 and not 9.
>
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
>
> just like how partch added on to his 31 tone diamond

You mean 29 tone diamond?

> to get his 43 tone
> scale, you have to add the pitches in question.

Ah, so you agree. That's what was missing in your original message.

> The point is though it shows how one can make a diamond out of a
scale
> on something besides the octave, which i am sorry that you missed.

Read my post again. I explicitly stated that certain notes were
equivalent (in the same box in the diamond) because '1' is equivalent
to '3' in the BP world. And it was clear to me that this was the 3-5-
7 diamond in ttritave-equivalence world. So what did I miss?

> one of the simplest , although quite musical method is to take the
MOS
> you scales implies as being next, count out that many tones and
take the
> number of tones in your scale as a subset.
> for instance with 12 ET we could consider the next MOS being 19 if
we
> were yassar.
> one then take 19 tones, which forms the octave and fifth and take
a 12
> tone subset of this.
> now if we take this idea further
> One could take the 13 tone BP scale and find the next constant
> structure and create another point of equivalence within this
already
> different one.

Thanks, Kraig. Sounds interesting but without examples I'm unable to
follow your meaning. Could you provide some examples?

The 9 tone and 13 tone BP scales in JI are constant structures and
periodicity blocks, both with 245:243 as one of the unison vectors.
Is the "next" constant structure also going to have 245:243 as one of
the unison vectors? If so, what's the other unison vector defining
it? If not, I'm guessing 271 tones per octave is the "next" constant
structure? (I don't expect you to answer these questions right
now . . .)

Here's a TOP BP horagram which goes out well beyond 13 notes in case
it's of any interest:

/tuning/files/Erlich/bigbphor.gif